7^m+343/7^m=56

Solution for 7^m+343/7^m=56 equation:

7^m+343/7^m=56

We move all terms to the left:

7^m+343/7^m-(56)=0


Domain of the equation: 7^m!=0

m!=0/1

m!=0

m∈R


We multiply all the terms by the denominator


7^m*7^m-56*7^m+343=0

Wy multiply elements

49m^2-392m+343=0

a = 49; b = -392; c = +343;
Δ = b2-4ac
Δ = -3922-4·49·343
Δ = 86436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{86436}=294$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-392)-294}{2*49}=\frac{98}{98}
=1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-392)+294}{2*49}=\frac{686}{98}
=7
$